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Math Help - Probability assistance required

  1. #1
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    Probability assistance required

    The question:

    Down's syndrome is a disorder that affects 1 in 270 babies born to mothers aged 35 or over. A new blood test for the condition has a sensitivity (i.e. the probability of a positive test result given the Down's syndrome is present) of 89%, The specificity (i.e. the probability of a negative test result given that Down's syndrome is absent) of the new test is 75%.

    a) What proportion of women over the age 35 would test positive on this new blood test?
    b) A mother over age 35 receives a positive test result. What is the chance that Down's syndrome is actually present?
    c) A mother over age 35 receives a negative test result. What is the chance that Down's syndrome is actually present.

    My attempt:
    For a) I managed to get the answer via a tree diagram, which is 25.237% However, I'm not sure how to attempt b) and c). How should I attempt this? Thanks
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  2. #2
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    Just in case a picture helps...

    If you can see how your tree diagram relates to this one...



    (with P = testing positive for the Down's, N = testing negative, D = Down's present, A = Down's absent)

    ... then you might be able to see how I've rearranged it again here...



    ... and how to use this.

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  3. #3
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    Hmm, my tree is different. I made each branch a fraction:



    Yours is confusing me. :/
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  4. #4
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    I ended up working it out using Bayes Rule. I'd still like to understand how to do it via a tree diagram though.
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  5. #5
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    Quote Originally Posted by Glitch View Post
    I ended up working it out using Bayes Rule. I'd still like to understand how to do it via a tree diagram though.
    Right! The tree method is a good way of understanding Bayes.

    Compare yours with my first. I used 89% and 11% like you, but imagined that was 89 mothers and 11 mothers, making 100 in all. Then 269 times as many as these is 26900, and we share these 25:75.

    (I.e. replace probabilities with possible quantities, as recommended in passing but curiously not exemplified here Conditional probability - Wikipedia, the free encyclopedia under 'The Conditional Probability Fallacy').

    This way we get a venn-diagram sense of the probabilities. The second tree is I think slightly better than rearranging the venn-diagram itself as here http://www.mathhelpforum.com/math-he...ty-169248.html. (Also http://www.mathhelpforum.com/math-he...on-169053.html).
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  6. #6
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    Ahh I see. So to get the solution to b), it's just a matter of 89/6814. I should try a few more questions. Thanks.
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